<!DOCTYPE html>
<!-- saved from url=(0058)https://mathjax.github.io/MathJax-demos-web/mml-chtml.html -->
<html lang="en" xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
    <head>
        <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
        <meta http-equiv="x-ua-compatible" content="ie=edge" />
        <meta name="viewport" content="width=device-width" />
        <title>
            MathJax v3 with MathML input and HTML output
        </title>
        <script id="MathJax-script" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/mml-chtml.js"></script>
        <style type="text/css">
        /*<![CDATA[*/
        .CtxtMenu_InfoClose {  top:.2em; right:.2em;}
        .CtxtMenu_InfoContent {  overflow:auto; text-align:left; font-size:80%;  padding:.4em .6em; border:1px inset; margin:1em 0px;  max-height:20em; max-width:30em; background-color:#EEEEEE;  white-space:normal;}
        .CtxtMenu_Info.CtxtMenu_MousePost {outline:none;}
        .CtxtMenu_Info {  position:fixed; left:50%; width:auto; text-align:center;  border:3px outset; padding:1em 2em; background-color:#DDDDDD;  color:black;  cursor:default; font-family:message-box; font-size:120%;  font-style:normal; text-indent:0; text-transform:none;  line-height:normal; letter-spacing:normal; word-spacing:normal;  word-wrap:normal; white-space:nowrap; float:none; z-index:201;  border-radius: 15px;                     /* Opera 10.5 and IE9 */  -webkit-border-radius:15px;               /* Safari and Chrome */  -moz-border-radius:15px;                  /* Firefox */  -khtml-border-radius:15px;                /* Konqueror */  box-shadow:0px 10px 20px #808080;         /* Opera 10.5 and IE9 */  -webkit-box-shadow:0px 10px 20px #808080; /* Safari 3 & Chrome */  -moz-box-shadow:0px 10px 20px #808080;    /* Forefox 3.5 */  -khtml-box-shadow:0px 10px 20px #808080;  /* Konqueror */  filter:progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color="gray", Positive="true"); /* IE */}
        /*]]>*/
        </style>
        <style type="text/css">
        /*<![CDATA[*/
        .CtxtMenu_MenuClose {  position:absolute;  cursor:pointer;  display:inline-block;  border:2px solid #AAA;  border-radius:18px;  -webkit-border-radius: 18px;             /* Safari and Chrome */  -moz-border-radius: 18px;                /* Firefox */  -khtml-border-radius: 18px;              /* Konqueror */  font-family: "Courier New", Courier;  font-size:24px;  color:#F0F0F0}
        .CtxtMenu_MenuClose span {  display:block; background-color:#AAA; border:1.5px solid;  border-radius:18px;  -webkit-border-radius: 18px;             /* Safari and Chrome */  -moz-border-radius: 18px;                /* Firefox */  -khtml-border-radius: 18px;              /* Konqueror */  line-height:0;  padding:8px 0 6px     /* may need to be browser-specific */}
        .CtxtMenu_MenuClose:hover {  color:white!important;  border:2px solid #CCC!important}
        .CtxtMenu_MenuClose:hover span {  background-color:#CCC!important}
        .CtxtMenu_MenuClose:hover:focus {  outline:none}
        /*]]>*/
        </style>
        <style type="text/css">
        /*<![CDATA[*/
        .CtxtMenu_Menu {  position:absolute;  background-color:white;  color:black;  width:auto; padding:5px 0px;  border:1px solid #CCCCCC; margin:0; cursor:default;  font: menu; text-align:left; text-indent:0; text-transform:none;  line-height:normal; letter-spacing:normal; word-spacing:normal;  word-wrap:normal; white-space:nowrap; float:none; z-index:201;  border-radius: 5px;                     /* Opera 10.5 and IE9 */  -webkit-border-radius: 5px;             /* Safari and Chrome */  -moz-border-radius: 5px;                /* Firefox */  -khtml-border-radius: 5px;              /* Konqueror */  box-shadow:0px 10px 20px #808080;         /* Opera 10.5 and IE9 */  -webkit-box-shadow:0px 10px 20px #808080; /* Safari 3 & Chrome */  -moz-box-shadow:0px 10px 20px #808080;    /* Forefox 3.5 */  -khtml-box-shadow:0px 10px 20px #808080;  /* Konqueror */}
        .CtxtMenu_MenuItem {  padding: 1px 2em;  background:transparent;}
        .CtxtMenu_MenuArrow {  position:absolute; right:.5em; padding-top:.25em; color:#666666;  font-family: null; font-size: .75em}
        .CtxtMenu_MenuActive .CtxtMenu_MenuArrow {color:white}
        .CtxtMenu_MenuArrow.CtxtMenu_RTL {left:.5em; right:auto}
        .CtxtMenu_MenuCheck {  position:absolute; left:.7em;  font-family: null}
        .CtxtMenu_MenuCheck.CtxtMenu_RTL { right:.7em; left:auto }
        .CtxtMenu_MenuRadioCheck {  position:absolute; left: .7em;}
        .CtxtMenu_MenuRadioCheck.CtxtMenu_RTL {  right: .7em; left:auto}
        .CtxtMenu_MenuInputBox {  padding-left: 1em; right:.5em; color:#666666;  font-family: null;}
        .CtxtMenu_MenuInputBox.CtxtMenu_RTL {  left: .1em;}
        .CtxtMenu_MenuComboBox {  left:.1em; padding-bottom:.5em;}
        .CtxtMenu_MenuSlider {  left: .1em;}
        .CtxtMenu_SliderValue {  position:absolute; right:.1em; padding-top:.25em; color:#333333;  font-size: .75em}
        .CtxtMenu_SliderBar {  outline: none; background: #d3d3d3}
        .CtxtMenu_MenuLabel {  padding: 1px 2em 3px 1.33em;  font-style:italic}
        .CtxtMenu_MenuRule {  border-top: 1px solid #DDDDDD;  margin: 4px 3px;}
        .CtxtMenu_MenuDisabled {  color:GrayText}
        .CtxtMenu_MenuActive {  background-color: #606872;  color: white;}
        .CtxtMenu_MenuDisabled:focus {  background-color: #E8E8E8}
        .CtxtMenu_MenuLabel:focus {  background-color: #E8E8E8}
        .CtxtMenu_ContextMenu:focus {  outline:none}
        .CtxtMenu_ContextMenu .CtxtMenu_MenuItem:focus {  outline:none}
        .CtxtMenu_SelectionMenu {  position:relative; float:left;  border-bottom: none; -webkit-box-shadow:none; -webkit-border-radius:0px; }
        .CtxtMenu_SelectionItem {  padding-right: 1em;}
        .CtxtMenu_Selection {  right: 40%; width:50%; }
        .CtxtMenu_SelectionBox {  padding: 0em; max-height:20em; max-width: none;  background-color:#FFFFFF;}
        .CtxtMenu_SelectionDivider {  clear: both; border-top: 2px solid #000000;}
        .CtxtMenu_Menu .CtxtMenu_MenuClose {  top:-10px; left:-10px}
        /*]]>*/
        </style>
        <style id="MJX-CHTML-styles">
        <![CDATA[
        mjx-container[jax="CHTML"] {
        line-height: 0;
        }

        mjx-container [space="1"] {
        margin-left: .111em;
        }

        mjx-container [space="2"] {
        margin-left: .167em;
        }

        mjx-container [space="3"] {
        margin-left: .222em;
        }

        mjx-container [space="4"] {
        margin-left: .278em;
        }

        mjx-container [space="5"] {
        margin-left: .333em;
        }

        mjx-container [rspace="1"] {
        margin-right: .111em;
        }

        mjx-container [rspace="2"] {
        margin-right: .167em;
        }

        mjx-container [rspace="3"] {
        margin-right: .222em;
        }

        mjx-container [rspace="4"] {
        margin-right: .278em;
        }

        mjx-container [rspace="5"] {
        margin-right: .333em;
        }

        mjx-container [size="s"] {
        font-size: 70.7%;
        }

        mjx-container [size="ss"] {
        font-size: 50%;
        }

        mjx-container [size="Tn"] {
        font-size: 60%;
        }

        mjx-container [size="sm"] {
        font-size: 85%;
        }

        mjx-container [size="lg"] {
        font-size: 120%;
        }

        mjx-container [size="Lg"] {
        font-size: 144%;
        }

        mjx-container [size="LG"] {
        font-size: 173%;
        }

        mjx-container [size="hg"] {
        font-size: 207%;
        }

        mjx-container [size="HG"] {
        font-size: 249%;
        }

        mjx-container [width="full"] {
        width: 100%;
        }

        mjx-box {
        display: inline-block;
        }

        mjx-block {
        display: block;
        }

        mjx-itable {
        display: inline-table;
        }

        mjx-row {
        display: table-row;
        }

        mjx-row > * {
        display: table-cell;
        }

        mjx-mtext {
        display: inline-block;
        text-align: left;
        }

        mjx-mstyle {
        display: inline-block;
        }

        mjx-merror {
        display: inline-block;
        color: red;
        background-color: yellow;
        }

        mjx-mphantom {
        visibility: hidden;
        }

        _::-webkit-full-page-media, _:future, :root mjx-container {
        will-change: opacity;
        }

        mjx-assistive-mml {
        position: absolute !important;
        top: 0px;
        left: 0px;
        clip: rect(1px, 1px, 1px, 1px);
        padding: 1px 0px 0px 0px !important;
        border: 0px !important;
        display: block !important;
        width: auto !important;
        overflow: hidden !important;
        -webkit-touch-callout: none;
        -webkit-user-select: none;
        -khtml-user-select: none;
        -moz-user-select: none;
        -ms-user-select: none;
        user-select: none;
        }

        mjx-assistive-mml[display="block"] {
        width: 100% !important;
        }

        mjx-math {
        display: inline-block;
        text-align: left;
        line-height: 0;
        text-indent: 0;
        font-style: normal;
        font-weight: normal;
        font-size: 100%;
        font-size-adjust: none;
        letter-spacing: normal;
        border-collapse: collapse;
        word-wrap: normal;
        word-spacing: normal;
        white-space: nowrap;
        direction: ltr;
        padding: 1px 0;
        }

        mjx-container[jax="CHTML"][display="true"] {
        display: block;
        text-align: center;
        margin: 1em 0;
        }

        mjx-container[jax="CHTML"][display="true"][width="full"] {
        display: flex;
        }

        mjx-container[jax="CHTML"][display="true"] mjx-math {
        padding: 0;
        }

        mjx-container[jax="CHTML"][justify="left"] {
        text-align: left;
        }

        mjx-container[jax="CHTML"][justify="right"] {
        text-align: right;
        }

        mjx-mi {
        display: inline-block;
        text-align: left;
        }

        mjx-c {
        display: inline-block;
        }

        mjx-utext {
        display: inline-block;
        padding: .75em 0 .2em 0;
        }

        mjx-mo {
        display: inline-block;
        text-align: left;
        }

        mjx-stretchy-h {
        display: inline-table;
        width: 100%;
        }

        mjx-stretchy-h > * {
        display: table-cell;
        width: 0;
        }

        mjx-stretchy-h > * > mjx-c {
        display: inline-block;
        transform: scalex(1.0000001);
        }

        mjx-stretchy-h > * > mjx-c::before {
        display: inline-block;
        width: initial;
        }

        mjx-stretchy-h > mjx-ext {
        /* IE */ overflow: hidden;
        /* others */ overflow: clip visible;
        width: 100%;
        }

        mjx-stretchy-h > mjx-ext > mjx-c::before {
        transform: scalex(500);
        }

        mjx-stretchy-h > mjx-ext > mjx-c {
        width: 0;
        }

        mjx-stretchy-h > mjx-beg > mjx-c {
        margin-right: -.1em;
        }

        mjx-stretchy-h > mjx-end > mjx-c {
        margin-left: -.1em;
        }

        mjx-stretchy-v {
        display: inline-block;
        }

        mjx-stretchy-v > * {
        display: block;
        }

        mjx-stretchy-v > mjx-beg {
        height: 0;
        }

        mjx-stretchy-v > mjx-end > mjx-c {
        display: block;
        }

        mjx-stretchy-v > * > mjx-c {
        transform: scaley(1.0000001);
        transform-origin: left center;
        overflow: hidden;
        }

        mjx-stretchy-v > mjx-ext {
        display: block;
        height: 100%;
        box-sizing: border-box;
        border: 0px solid transparent;
        /* IE */ overflow: hidden;
        /* others */ overflow: visible clip;
        }

        mjx-stretchy-v > mjx-ext > mjx-c::before {
        width: initial;
        box-sizing: border-box;
        }

        mjx-stretchy-v > mjx-ext > mjx-c {
        transform: scaleY(500) translateY(.075em);
        overflow: visible;
        }

        mjx-mark {
        display: inline-block;
        height: 0px;
        }

        mjx-mn {
        display: inline-block;
        text-align: left;
        }

        mjx-msup {
        display: inline-block;
        text-align: left;
        }

        mjx-mrow {
        display: inline-block;
        text-align: left;
        }

        mjx-mfrac {
        display: inline-block;
        text-align: left;
        }

        mjx-frac {
        display: inline-block;
        vertical-align: 0.17em;
        padding: 0 .22em;
        }

        mjx-frac[type="d"] {
        vertical-align: .04em;
        }

        mjx-frac[delims] {
        padding: 0 .1em;
        }

        mjx-frac[atop] {
        padding: 0 .12em;
        }

        mjx-frac[atop][delims] {
        padding: 0;
        }

        mjx-dtable {
        display: inline-table;
        width: 100%;
        }

        mjx-dtable > * {
        font-size: 2000%;
        }

        mjx-dbox {
        display: block;
        font-size: 5%;
        }

        mjx-num {
        display: block;
        text-align: center;
        }

        mjx-den {
        display: block;
        text-align: center;
        }

        mjx-mfrac[bevelled] > mjx-num {
        display: inline-block;
        }

        mjx-mfrac[bevelled] > mjx-den {
        display: inline-block;
        }

        mjx-den[align="right"], mjx-num[align="right"] {
        text-align: right;
        }

        mjx-den[align="left"], mjx-num[align="left"] {
        text-align: left;
        }

        mjx-nstrut {
        display: inline-block;
        height: .054em;
        width: 0;
        vertical-align: -.054em;
        }

        mjx-nstrut[type="d"] {
        height: .217em;
        vertical-align: -.217em;
        }

        mjx-dstrut {
        display: inline-block;
        height: .505em;
        width: 0;
        }

        mjx-dstrut[type="d"] {
        height: .726em;
        }

        mjx-line {
        display: block;
        box-sizing: border-box;
        min-height: 1px;
        height: .06em;
        border-top: .06em solid;
        margin: .06em -.1em;
        overflow: hidden;
        }

        mjx-line[type="d"] {
        margin: .18em -.1em;
        }

        mjx-msqrt {
        display: inline-block;
        text-align: left;
        }

        mjx-root {
        display: inline-block;
        white-space: nowrap;
        }

        mjx-surd {
        display: inline-block;
        vertical-align: top;
        }

        mjx-sqrt {
        display: inline-block;
        padding-top: .07em;
        }

        mjx-sqrt > mjx-box {
        border-top: .07em solid;
        }

        mjx-sqrt.mjx-tall > mjx-box {
        padding-left: .3em;
        margin-left: -.3em;
        }

        mjx-mtable {
        display: inline-block;
        text-align: center;
        vertical-align: .25em;
        position: relative;
        box-sizing: border-box;
        border-spacing: 0;
        border-collapse: collapse;
        }

        mjx-mstyle[size="s"] mjx-mtable {
        vertical-align: .354em;
        }

        mjx-labels {
        position: absolute;
        left: 0;
        top: 0;
        }

        mjx-table {
        display: inline-block;
        vertical-align: -.5ex;
        box-sizing: border-box;
        }

        mjx-table > mjx-itable {
        vertical-align: middle;
        text-align: left;
        box-sizing: border-box;
        }

        mjx-labels > mjx-itable {
        position: absolute;
        top: 0;
        }

        mjx-mtable[justify="left"] {
        text-align: left;
        }

        mjx-mtable[justify="right"] {
        text-align: right;
        }

        mjx-mtable[justify="left"][side="left"] {
        padding-right: 0 ! important;
        }

        mjx-mtable[justify="left"][side="right"] {
        padding-left: 0 ! important;
        }

        mjx-mtable[justify="right"][side="left"] {
        padding-right: 0 ! important;
        }

        mjx-mtable[justify="right"][side="right"] {
        padding-left: 0 ! important;
        }

        mjx-mtable[align] {
        vertical-align: baseline;
        }

        mjx-mtable[align="top"] > mjx-table {
        vertical-align: top;
        }

        mjx-mtable[align="bottom"] > mjx-table {
        vertical-align: bottom;
        }

        mjx-mtable[side="right"] mjx-labels {
        min-width: 100%;
        }

        mjx-mtr {
        display: table-row;
        text-align: left;
        }

        mjx-mtr[rowalign="top"] > mjx-mtd {
        vertical-align: top;
        }

        mjx-mtr[rowalign="center"] > mjx-mtd {
        vertical-align: middle;
        }

        mjx-mtr[rowalign="bottom"] > mjx-mtd {
        vertical-align: bottom;
        }

        mjx-mtr[rowalign="baseline"] > mjx-mtd {
        vertical-align: baseline;
        }

        mjx-mtr[rowalign="axis"] > mjx-mtd {
        vertical-align: .25em;
        }

        mjx-mtd {
        display: table-cell;
        text-align: center;
        padding: .215em .4em;
        }

        mjx-mtd:first-child {
        padding-left: 0;
        }

        mjx-mtd:last-child {
        padding-right: 0;
        }

        mjx-mtable > * > mjx-itable > *:first-child > mjx-mtd {
        padding-top: 0;
        }

        mjx-mtable > * > mjx-itable > *:last-child > mjx-mtd {
        padding-bottom: 0;
        }

        mjx-tstrut {
        display: inline-block;
        height: 1em;
        vertical-align: -.25em;
        }

        mjx-labels[align="left"] > mjx-mtr > mjx-mtd {
        text-align: left;
        }

        mjx-labels[align="right"] > mjx-mtr > mjx-mtd {
        text-align: right;
        }

        mjx-mtd[extra] {
        padding: 0;
        }

        mjx-mtd[rowalign="top"] {
        vertical-align: top;
        }

        mjx-mtd[rowalign="center"] {
        vertical-align: middle;
        }

        mjx-mtd[rowalign="bottom"] {
        vertical-align: bottom;
        }

        mjx-mtd[rowalign="baseline"] {
        vertical-align: baseline;
        }

        mjx-mtd[rowalign="axis"] {
        vertical-align: .25em;
        }

        mjx-TeXAtom {
        display: inline-block;
        text-align: left;
        }

        mjx-mover {
        display: inline-block;
        text-align: left;
        }

        mjx-mover:not([limits="false"]) {
        padding-top: .1em;
        }

        mjx-mover:not([limits="false"]) > * {
        display: block;
        text-align: left;
        }

        mjx-munderover {
        display: inline-block;
        text-align: left;
        }

        mjx-munderover:not([limits="false"]) {
        padding-top: .1em;
        }

        mjx-munderover:not([limits="false"]) > * {
        display: block;
        }

        mjx-msubsup {
        display: inline-block;
        text-align: left;
        }

        mjx-script {
        display: inline-block;
        padding-right: .05em;
        padding-left: .033em;
        }

        mjx-script > mjx-spacer {
        display: block;
        }

        mjx-msub {
        display: inline-block;
        text-align: left;
        }

        mjx-mspace {
        display: inline-block;
        text-align: left;
        }

        mjx-c::before {
        display: block;
        width: 0;
        }

        .MJX-TEX {
        font-family: MJXZERO, MJXTEX;
        }

        .TEX-B {
        font-family: MJXZERO, MJXTEX-B;
        }

        .TEX-I {
        font-family: MJXZERO, MJXTEX-I;
        }

        .TEX-MI {
        font-family: MJXZERO, MJXTEX-MI;
        }

        .TEX-BI {
        font-family: MJXZERO, MJXTEX-BI;
        }

        .TEX-S1 {
        font-family: MJXZERO, MJXTEX-S1;
        }

        .TEX-S2 {
        font-family: MJXZERO, MJXTEX-S2;
        }

        .TEX-S3 {
        font-family: MJXZERO, MJXTEX-S3;
        }

        .TEX-S4 {
        font-family: MJXZERO, MJXTEX-S4;
        }

        .TEX-A {
        font-family: MJXZERO, MJXTEX-A;
        }

        .TEX-C {
        font-family: MJXZERO, MJXTEX-C;
        }

        .TEX-CB {
        font-family: MJXZERO, MJXTEX-CB;
        }

        .TEX-FR {
        font-family: MJXZERO, MJXTEX-FR;
        }

        .TEX-FRB {
        font-family: MJXZERO, MJXTEX-FRB;
        }

        .TEX-SS {
        font-family: MJXZERO, MJXTEX-SS;
        }

        .TEX-SSB {
        font-family: MJXZERO, MJXTEX-SSB;
        }

        .TEX-SSI {
        font-family: MJXZERO, MJXTEX-SSI;
        }

        .TEX-SC {
        font-family: MJXZERO, MJXTEX-SC;
        }

        .TEX-T {
        font-family: MJXZERO, MJXTEX-T;
        }

        .TEX-V {
        font-family: MJXZERO, MJXTEX-V;
        }

        .TEX-VB {
        font-family: MJXZERO, MJXTEX-VB;
        }

        mjx-stretchy-v mjx-c, mjx-stretchy-h mjx-c {
        font-family: MJXZERO, MJXTEX-S1, MJXTEX-S4, MJXTEX, MJXTEX-A ! important;
        }

        @font-face /* 0 */ {
        font-family: MJXZERO;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Zero.woff") format("woff");
        }

        @font-face /* 1 */ {
        font-family: MJXTEX;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Regular.woff") format("woff");
        }

        @font-face /* 2 */ {
        font-family: MJXTEX-B;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Bold.woff") format("woff");
        }

        @font-face /* 3 */ {
        font-family: MJXTEX-I;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Math-Italic.woff") format("woff");
        }

        @font-face /* 4 */ {
        font-family: MJXTEX-MI;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Italic.woff") format("woff");
        }

        @font-face /* 5 */ {
        font-family: MJXTEX-BI;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Math-BoldItalic.woff") format("woff");
        }

        @font-face /* 6 */ {
        font-family: MJXTEX-S1;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size1-Regular.woff") format("woff");
        }

        @font-face /* 7 */ {
        font-family: MJXTEX-S2;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size2-Regular.woff") format("woff");
        }

        @font-face /* 8 */ {
        font-family: MJXTEX-S3;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size3-Regular.woff") format("woff");
        }

        @font-face /* 9 */ {
        font-family: MJXTEX-S4;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size4-Regular.woff") format("woff");
        }

        @font-face /* 10 */ {
        font-family: MJXTEX-A;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_AMS-Regular.woff") format("woff");
        }

        @font-face /* 11 */ {
        font-family: MJXTEX-C;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Calligraphic-Regular.woff") format("woff");
        }

        @font-face /* 12 */ {
        font-family: MJXTEX-CB;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Calligraphic-Bold.woff") format("woff");
        }

        @font-face /* 13 */ {
        font-family: MJXTEX-FR;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Fraktur-Regular.woff") format("woff");
        }

        @font-face /* 14 */ {
        font-family: MJXTEX-FRB;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Fraktur-Bold.woff") format("woff");
        }

        @font-face /* 15 */ {
        font-family: MJXTEX-SS;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Regular.woff") format("woff");
        }

        @font-face /* 16 */ {
        font-family: MJXTEX-SSB;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Bold.woff") format("woff");
        }

        @font-face /* 17 */ {
        font-family: MJXTEX-SSI;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Italic.woff") format("woff");
        }

        @font-face /* 18 */ {
        font-family: MJXTEX-SC;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Script-Regular.woff") format("woff");
        }

        @font-face /* 19 */ {
        font-family: MJXTEX-T;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Typewriter-Regular.woff") format("woff");
        }

        @font-face /* 20 */ {
        font-family: MJXTEX-V;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Regular.woff") format("woff");
        }

        @font-face /* 21 */ {
        font-family: MJXTEX-VB;
        src: url("https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Bold.woff") format("woff");
        }

        mjx-stretchy-v.mjx-c7C mjx-ext mjx-c::before {
        content: "\2223";
        width: 0.333em;
        }

        mjx-c.mjx-c1D44E.TEX-I::before {
        padding: 0.441em 0.529em 0.01em 0;
        content: "a";
        }

        mjx-c.mjx-c2260::before {
        padding: 0.716em 0.778em 0.215em 0;
        content: "\2260";
        }

        mjx-c.mjx-c30::before {
        padding: 0.666em 0.5em 0.022em 0;
        content: "0";
        }

        mjx-c.mjx-c1D465.TEX-I::before {
        padding: 0.442em 0.572em 0.011em 0;
        content: "x";
        }

        mjx-c.mjx-c32::before {
        padding: 0.666em 0.5em 0 0;
        content: "2";
        }

        mjx-c.mjx-c2B::before {
        padding: 0.583em 0.778em 0.082em 0;
        content: "+";
        }

        mjx-c.mjx-c1D44F.TEX-I::before {
        padding: 0.694em 0.429em 0.011em 0;
        content: "b";
        }

        mjx-c.mjx-c1D450.TEX-I::before {
        padding: 0.442em 0.433em 0.011em 0;
        content: "c";
        }

        mjx-c.mjx-c3D::before {
        padding: 0.583em 0.778em 0.082em 0;
        content: "=";
        }

        mjx-c.mjx-c2212::before {
        padding: 0.583em 0.778em 0.082em 0;
        content: "\2212";
        }

        mjx-c.mjx-cB1::before {
        padding: 0.666em 0.778em 0 0;
        content: "\B1";
        }

        mjx-c.mjx-c221A::before {
        padding: 0.8em 0.853em 0.2em 0;
        content: "\221A";
        }

        mjx-c.mjx-c34::before {
        padding: 0.677em 0.5em 0 0;
        content: "4";
        }

        mjx-c.mjx-c2E::before {
        padding: 0.12em 0.278em 0 0;
        content: ".";
        }

        mjx-c.mjx-c2D9::before {
        padding: 0.669em 0.5em 0 0;
        content: "\2D9";
        }

        mjx-c.mjx-c1D70E.TEX-I::before {
        padding: 0.431em 0.571em 0.011em 0;
        content: "\3C3";
        }

        mjx-c.mjx-c28::before {
        padding: 0.75em 0.389em 0.25em 0;
        content: "(";
        }

        mjx-c.mjx-c1D466.TEX-I::before {
        padding: 0.442em 0.49em 0.205em 0;
        content: "y";
        }

        mjx-c.mjx-c29::before {
        padding: 0.75em 0.389em 0.25em 0;
        content: ")";
        }

        mjx-c.mjx-c1D70C.TEX-I::before {
        padding: 0.442em 0.517em 0.216em 0;
        content: "\3C1";
        }

        mjx-c.mjx-c1D467.TEX-I::before {
        padding: 0.442em 0.465em 0.011em 0;
        content: "z";
        }

        mjx-c.mjx-c1D6FD.TEX-I::before {
        padding: 0.705em 0.566em 0.194em 0;
        content: "\3B2";
        }

        mjx-c.mjx-c28.TEX-S4::before {
        padding: 1.75em 0.792em 1.249em 0;
        content: "(";
        }

        mjx-c.mjx-c1D45B.TEX-I::before {
        padding: 0.442em 0.6em 0.011em 0;
        content: "n";
        }

        mjx-c.mjx-c2211.TEX-S2::before {
        padding: 0.95em 1.444em 0.45em 0;
        content: "\2211";
        }

        mjx-c.mjx-c1D458.TEX-I::before {
        padding: 0.694em 0.521em 0.011em 0;
        content: "k";
        }

        mjx-c.mjx-c31::before {
        padding: 0.666em 0.5em 0 0;
        content: "1";
        }

        mjx-c.mjx-c29.TEX-S4::before {
        padding: 1.75em 0.792em 1.249em 0;
        content: ")";
        }

        mjx-c.mjx-c2264::before {
        padding: 0.636em 0.778em 0.138em 0;
        content: "\2264";
        }

        mjx-c.mjx-c1D415.TEX-B::before {
        padding: 0.686em 0.869em 0.007em 0;
        content: "V";
        }

        mjx-c.mjx-cD7::before {
        padding: 0.491em 0.778em 0 0;
        content: "\D7";
        }

        mjx-c.mjx-c1D422.TEX-B::before {
        padding: 0.695em 0.319em 0 0;
        content: "i";
        }

        mjx-c.mjx-c1D423.TEX-B::before {
        padding: 0.695em 0.351em 0.2em 0;
        content: "j";
        }

        mjx-c.mjx-c1D424.TEX-B::before {
        padding: 0.694em 0.607em 0 0;
        content: "k";
        }

        mjx-c.mjx-c2202::before {
        padding: 0.715em 0.566em 0.022em 0;
        content: "\2202";
        }

        mjx-c.mjx-c1D44B.TEX-I::before {
        padding: 0.683em 0.852em 0 0;
        content: "X";
        }

        mjx-c.mjx-c1D462.TEX-I::before {
        padding: 0.442em 0.572em 0.011em 0;
        content: "u";
        }

        mjx-c.mjx-c1D44C.TEX-I::before {
        padding: 0.683em 0.763em 0 0;
        content: "Y";
        }

        mjx-c.mjx-c1D463.TEX-I::before {
        padding: 0.443em 0.485em 0.011em 0;
        content: "v";
        }

        mjx-c.mjx-c1D443.TEX-I::before {
        padding: 0.683em 0.751em 0 0;
        content: "P";
        }

        mjx-c.mjx-c1D438.TEX-I::before {
        padding: 0.68em 0.764em 0 0;
        content: "E";
        }

        mjx-c.mjx-c28.TEX-S3::before {
        padding: 1.45em 0.736em 0.949em 0;
        content: "(";
        }

        mjx-c.mjx-c29.TEX-S3::before {
        padding: 1.45em 0.736em 0.949em 0;
        content: ")";
        }

        mjx-c.mjx-c1D45D.TEX-I::before {
        padding: 0.442em 0.503em 0.194em 0;
        content: "p";
        }

        mjx-c.mjx-c221A.TEX-S2::before {
        padding: 1.15em 1.02em 0.65em 0;
        content: "\221A";
        }

        mjx-c.mjx-c1D719.TEX-I::before {
        padding: 0.694em 0.596em 0.205em 0;
        content: "\3D5";
        }

        mjx-c.mjx-c35::before {
        padding: 0.666em 0.5em 0.022em 0;
        content: "5";
        }

        mjx-c.mjx-c1D452.TEX-I::before {
        padding: 0.442em 0.466em 0.011em 0;
        content: "e";
        }

        mjx-c.mjx-c1D70B.TEX-I::before {
        padding: 0.431em 0.57em 0.011em 0;
        content: "\3C0";
        }

        mjx-c.mjx-c36::before {
        padding: 0.666em 0.5em 0.022em 0;
        content: "6";
        }

        mjx-c.mjx-c38::before {
        padding: 0.666em 0.5em 0.022em 0;
        content: "8";
        }

        mjx-c.mjx-c2026::before {
        padding: 0.12em 1.172em 0 0;
        content: "\2026";
        }

        mjx-c.mjx-c1D45E.TEX-I::before {
        padding: 0.442em 0.46em 0.194em 0;
        content: "q";
        }

        mjx-c.mjx-c22EF::before {
        padding: 0.31em 1.172em 0 0;
        content: "\22EF";
        }

        mjx-c.mjx-c221E::before {
        padding: 0.442em 1em 0.011em 0;
        content: "\221E";
        }

        mjx-c.mjx-c220F.TEX-S2::before {
        padding: 0.95em 1.278em 0.45em 0;
        content: "\220F";
        }

        mjx-c.mjx-c1D457.TEX-I::before {
        padding: 0.661em 0.412em 0.204em 0;
        content: "j";
        }

        mjx-c.mjx-c33::before {
        padding: 0.665em 0.5em 0.022em 0;
        content: "3";
        }

        mjx-c.mjx-c2C::before {
        padding: 0.121em 0.278em 0.194em 0;
        content: ",";
        }

        mjx-c.mjx-c66::before {
        padding: 0.705em 0.372em 0 0;
        content: "f";
        }

        mjx-c.mjx-c6F::before {
        padding: 0.448em 0.5em 0.01em 0;
        content: "o";
        }

        mjx-c.mjx-c72::before {
        padding: 0.442em 0.392em 0 0;
        content: "r";
        }

        mjx-c.mjx-cA0::before {
        padding: 0 0.25em 0 0;
        content: "\A0";
        }

        mjx-c.mjx-c7C::before {
        padding: 0.75em 0.278em 0.249em 0;
        content: "|";
        }

        mjx-c.mjx-c3C::before {
        padding: 0.54em 0.778em 0.04em 0;
        content: "<";
        }

        mjx-c.mjx-c2207::before {
        padding: 0.683em 0.833em 0.033em 0;
        content: "\2207";
        }

        mjx-c.mjx-c20D7.TEX-V::before {
        padding: 0.714em 0.5em 0 0;
        content: "\2192";
        }

        mjx-c.mjx-c1D401.TEX-B::before {
        padding: 0.686em 0.818em 0 0;
        content: "B";
        }

        mjx-c.mjx-c1D404.TEX-B::before {
        padding: 0.68em 0.756em 0 0;
        content: "E";
        }

        mjx-c.mjx-c1D461.TEX-I::before {
        padding: 0.626em 0.361em 0.011em 0;
        content: "t";
        }

        mjx-c.mjx-c22C5::before {
        padding: 0.31em 0.278em 0 0;
        content: "\22C5";
        }

        mjx-c.mjx-c1D7CE.TEX-B::before {
        padding: 0.654em 0.575em 0.01em 0;
        content: "0";
        }
        ]]>
        </style>
    </head>
    <body>
        <h1>
            MathJax v3 beta: MathML input, HTML output test
        </h1>
        <p>
            When
        </p>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="0" style="font-size: 101.6%; position: relative;">
            <mjx-math class="MJX-TEX" aria-hidden="true">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n" space="4">
                    <mjx-c class="mjx-c2260"></mjx-c>
                </mjx-mo>
                <mjx-mn class="mjx-n" space="4">
                    <mjx-c class="mjx-c30"></mjx-c>
                </mjx-mn>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="inline">
                <math xmlns="http://www.w3.org/1998/Math/MathML">
                <mi>
                    a
                </mi>
                <mo>
                    ≠
                </mo>
                <mn>
                    0
                </mn></math>
            </mjx-assistive-mml>
        </mjx-container>, there are two solutions to
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="1" style="font-size: 101.6%; position: relative;">
            <mjx-math class="MJX-TEX" aria-hidden="true">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-msup>
                    <mjx-mi class="mjx-i">
                        <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                    </mjx-mi>
                    <mjx-script style="vertical-align: 0.363em;">
                        <mjx-mn class="mjx-n" size="s">
                            <mjx-c class="mjx-c32"></mjx-c>
                        </mjx-mn>
                    </mjx-script>
                </mjx-msup>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c2B"></mjx-c>
                </mjx-mo>
                <mjx-mi class="mjx-i" space="3">
                    <mjx-c class="mjx-c1D44F TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c2B"></mjx-c>
                </mjx-mo>
                <mjx-mi class="mjx-i" space="3">
                    <mjx-c class="mjx-c1D450 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n" space="4">
                    <mjx-c class="mjx-c3D"></mjx-c>
                </mjx-mo>
                <mjx-mn class="mjx-n" space="4">
                    <mjx-c class="mjx-c30"></mjx-c>
                </mjx-mn>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="inline">
                <math xmlns="http://www.w3.org/1998/Math/MathML">
                <mi>
                    a
                </mi>
                <msup>
                    <mi>
                        x
                    </mi>
                    <mn>
                        2
                    </mn>
                </msup>
                <mo>
                    +
                </mo>
                <mi>
                    b
                </mi>
                <mi>
                    x
                </mi>
                <mo>
                    +
                </mo>
                <mi>
                    c
                </mi>
                <mo>
                    =
                </mo>
                <mn>
                    0
                </mn></math>
            </mjx-assistive-mml>
        </mjx-container>and they are
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" display="true" tabindex="0" ctxtmenu_counter="2" style="font-size: 101.6%; position: relative;">
            <mjx-math display="true" class="MJX-TEX" aria-hidden="true" style="margin-left: 0px; margin-right: 0px;">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n" space="4">
                    <mjx-c class="mjx-c3D"></mjx-c>
                </mjx-mo>
                <mjx-mrow space="4">
                    <mjx-mfrac>
                        <mjx-frac type="d">
                            <mjx-num>
                                <mjx-nstrut type="d"></mjx-nstrut>
                                <mjx-mrow>
                                    <mjx-mo class="mjx-n">
                                        <mjx-c class="mjx-c2212"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D44F TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mo class="mjx-n" space="3">
                                        <mjx-c class="mjx-cB1"></mjx-c>
                                    </mjx-mo>
                                    <mjx-msqrt space="3">
                                        <mjx-sqrt>
                                            <mjx-surd>
                                                <mjx-mo class="mjx-n">
                                                    <mjx-c class="mjx-c221A"></mjx-c>
                                                </mjx-mo>
                                            </mjx-surd>
                                            <mjx-box style="padding-top: 0.087em;">
                                                <mjx-msup>
                                                    <mjx-mi class="mjx-i">
                                                        <mjx-c class="mjx-c1D44F TEX-I"></mjx-c>
                                                    </mjx-mi>
                                                    <mjx-script style="vertical-align: 0.289em;">
                                                        <mjx-mn class="mjx-n" size="s">
                                                            <mjx-c class="mjx-c32"></mjx-c>
                                                        </mjx-mn>
                                                    </mjx-script>
                                                </mjx-msup>
                                                <mjx-mo class="mjx-n" space="3">
                                                    <mjx-c class="mjx-c2212"></mjx-c>
                                                </mjx-mo>
                                                <mjx-mn class="mjx-n" space="3">
                                                    <mjx-c class="mjx-c34"></mjx-c>
                                                </mjx-mn>
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                                                </mjx-mi>
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D450 TEX-I"></mjx-c>
                                                </mjx-mi>
                                            </mjx-box>
                                        </mjx-sqrt>
                                    </mjx-msqrt>
                                </mjx-mrow>
                            </mjx-num>
                            <mjx-dbox>
                                <mjx-dtable>
                                    <mjx-line type="d"></mjx-line>
                                    <mjx-row>
                                        <mjx-den>
                                            <mjx-dstrut type="d"></mjx-dstrut>
                                            <mjx-mrow>
                                                <mjx-mn class="mjx-n">
                                                    <mjx-c class="mjx-c32"></mjx-c>
                                                </mjx-mn>
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                                                </mjx-mi>
                                            </mjx-mrow>
                                        </mjx-den>
                                    </mjx-row>
                                </mjx-dtable>
                            </mjx-dbox>
                        </mjx-frac>
                    </mjx-mfrac>
                </mjx-mrow>
                <mjx-mtext class="mjx-n">
                    <mjx-c class="mjx-c2E"></mjx-c>
                </mjx-mtext>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <mi>
                    x
                </mi>
                <mo>
                    =
                </mo>
                <mrow>
                    <mfrac>
                        <mrow>
                            <mo>
                                −
                            </mo>
                            <mi>
                                b
                            </mi>
                            <mo>
                                ±
                            </mo>
                            <msqrt>
                                <msup>
                                    <mi>
                                        b
                                    </mi>
                                    <mn>
                                        2
                                    </mn>
                                </msup>
                                <mo>
                                    −
                                </mo>
                                <mn>
                                    4
                                </mn>
                                <mi>
                                    a
                                </mi>
                                <mi>
                                    c
                                </mi>
                            </msqrt>
                        </mrow>
                        <mrow>
                            <mn>
                                2
                            </mn>
                            <mi>
                                a
                            </mi>
                        </mrow>
                    </mfrac>
                </mrow>
                <mtext>
                    .
                </mtext></math>
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        </mjx-container>
        <h2>
            The Lorenz Equations
        </h2>
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                                                    <mjx-c class="mjx-c2D9"></mjx-c>
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                                    <mjx-tstrut></mjx-tstrut>
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                                        <mjx-c class="mjx-c2212"></mjx-c>
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                                        <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
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                                        <mjx-c class="mjx-c29"></mjx-c>
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                                    <mjx-tstrut></mjx-tstrut>
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                            </mjx-mtr>
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                                                    <mjx-c class="mjx-c2D9"></mjx-c>
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                                            <mjx-base>
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D466 TEX-I"></mjx-c>
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                                    <mjx-tstrut></mjx-tstrut>
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                                <mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em; padding-bottom: 0.15em;">
                                    <mjx-mi class="mjx-n"></mjx-mi>
                                    <mjx-mo class="mjx-n" space="4">
                                        <mjx-c class="mjx-c3D"></mjx-c>
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                                    <mjx-mi class="mjx-i" space="4">
                                        <mjx-c class="mjx-c1D70C TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mo class="mjx-n" space="3">
                                        <mjx-c class="mjx-c2212"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mi class="mjx-i" space="3">
                                        <mjx-c class="mjx-c1D466 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mo class="mjx-n" space="3">
                                        <mjx-c class="mjx-c2212"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mi class="mjx-i" space="3">
                                        <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D467 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                            </mjx-mtr>
                            <mjx-mtr>
                                <mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em;">
                                    <mjx-texatom texclass="ORD">
                                        <mjx-mover>
                                            <mjx-over style="padding-bottom: 0.105em; padding-left: 0.288em; margin-bottom: -0.549em;">
                                                <mjx-mo class="mjx-n" style="width: 0px; margin-left: -0.25em;">
                                                    <mjx-c class="mjx-c2D9"></mjx-c>
                                                </mjx-mo>
                                            </mjx-over>
                                            <mjx-base>
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D467 TEX-I"></mjx-c>
                                                </mjx-mi>
                                            </mjx-base>
                                        </mjx-mover>
                                    </mjx-texatom>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                                <mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em;">
                                    <mjx-mi class="mjx-n"></mjx-mi>
                                    <mjx-mo class="mjx-n" space="4">
                                        <mjx-c class="mjx-c3D"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mo class="mjx-n" space="4">
                                        <mjx-c class="mjx-c2212"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D6FD TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D467 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mo class="mjx-n" space="3">
                                        <mjx-c class="mjx-c2B"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mi class="mjx-i" space="3">
                                        <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D466 TEX-I"></mjx-c>
                                    </mjx-mi>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                            </mjx-mtr>
                        </mjx-itable>
                    </mjx-table>
                </mjx-mtable>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
                    <mtr>
                        <mtd>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mi>
                                        x
                                    </mi>
                                    <mo>
                                        ˙
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mi>
                                σ
                            </mi>
                            <mo stretchy="false">
                                (
                            </mo>
                            <mi>
                                y
                            </mi>
                            <mo>
                                −
                            </mo>
                            <mi>
                                x
                            </mi>
                            <mo stretchy="false">
                                )
                            </mo>
                        </mtd>
                    </mtr>
                    <mtr>
                        <mtd>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mi>
                                        y
                                    </mi>
                                    <mo>
                                        ˙
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mi>
                                ρ
                            </mi>
                            <mi>
                                x
                            </mi>
                            <mo>
                                −
                            </mo>
                            <mi>
                                y
                            </mi>
                            <mo>
                                −
                            </mo>
                            <mi>
                                x
                            </mi>
                            <mi>
                                z
                            </mi>
                        </mtd>
                    </mtr>
                    <mtr>
                        <mtd>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mi>
                                        z
                                    </mi>
                                    <mo>
                                        ˙
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mo>
                                −
                            </mo>
                            <mi>
                                β
                            </mi>
                            <mi>
                                z
                            </mi>
                            <mo>
                                +
                            </mo>
                            <mi>
                                x
                            </mi>
                            <mi>
                                y
                            </mi>
                        </mtd>
                    </mtr>
                </mtable></math>
            </mjx-assistive-mml>
        </mjx-container>
        <h2>
            The Cauchy-Schwarz Inequality
        </h2>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" display="true" tabindex="0" ctxtmenu_counter="4" style="font-size: 101.6%; position: relative;">
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                <mjx-msup>
                    <mjx-mrow>
                        <mjx-mo class="mjx-s4">
                            <mjx-c class="mjx-c28 TEX-S4"></mjx-c>
                        </mjx-mo>
                        <mjx-mrow>
                            <mjx-munderover>
                                <mjx-over style="padding-bottom: 0.192em; padding-left: 0.51em;">
                                    <mjx-mi class="mjx-i" size="s">
                                        <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                                    </mjx-mi>
                                </mjx-over>
                                <mjx-box>
                                    <mjx-munder>
                                        <mjx-row>
                                            <mjx-base>
                                                <mjx-mo class="mjx-lop">
                                                    <mjx-c class="mjx-c2211 TEX-S2"></mjx-c>
                                                </mjx-mo>
                                            </mjx-base>
                                        </mjx-row>
                                        <mjx-row>
                                            <mjx-under style="padding-top: 0.167em; padding-left: 0.086em;">
                                                <mjx-texatom size="s" texclass="ORD">
                                                    <mjx-mi class="mjx-i">
                                                        <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                                    </mjx-mi>
                                                    <mjx-mo class="mjx-n">
                                                        <mjx-c class="mjx-c3D"></mjx-c>
                                                    </mjx-mo>
                                                    <mjx-mn class="mjx-n">
                                                        <mjx-c class="mjx-c31"></mjx-c>
                                                    </mjx-mn>
                                                </mjx-texatom>
                                            </mjx-under>
                                        </mjx-row>
                                    </mjx-munder>
                                </mjx-box>
                            </mjx-munderover>
                            <mjx-msub space="2">
                                <mjx-mi class="mjx-i">
                                    <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                                </mjx-mi>
                                <mjx-script style="vertical-align: -0.15em;">
                                    <mjx-mi class="mjx-i" size="s">
                                        <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                    </mjx-mi>
                                </mjx-script>
                            </mjx-msub>
                            <mjx-msub>
                                <mjx-mi class="mjx-i">
                                    <mjx-c class="mjx-c1D44F TEX-I"></mjx-c>
                                </mjx-mi>
                                <mjx-script style="vertical-align: -0.15em;">
                                    <mjx-mi class="mjx-i" size="s">
                                        <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                    </mjx-mi>
                                </mjx-script>
                            </mjx-msub>
                        </mjx-mrow>
                        <mjx-mo class="mjx-s4">
                            <mjx-c class="mjx-c29 TEX-S4"></mjx-c>
                        </mjx-mo>
                    </mjx-mrow>
                    <mjx-script style="vertical-align: 1.477em;">
                        <mjx-texatom size="s" texclass="ORD" style="width: 0.167em;">
                            <mjx-mspace style="margin-right: -0.167em;"></mjx-mspace>
                            <mjx-mspace style="margin-right: -0.167em;"></mjx-mspace>
                            <mjx-mn class="mjx-n">
                                <mjx-c class="mjx-c32"></mjx-c>
                            </mjx-mn>
                        </mjx-texatom>
                    </mjx-script>
                </mjx-msup>
                <mjx-mo class="mjx-n" space="4">
                    <mjx-c class="mjx-c2264"></mjx-c>
                </mjx-mo>
                <mjx-mrow space="4">
                    <mjx-mo class="mjx-s4">
                        <mjx-c class="mjx-c28 TEX-S4"></mjx-c>
                    </mjx-mo>
                    <mjx-mrow>
                        <mjx-munderover>
                            <mjx-over style="padding-bottom: 0.192em; padding-left: 0.51em;">
                                <mjx-mi class="mjx-i" size="s">
                                    <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                                </mjx-mi>
                            </mjx-over>
                            <mjx-box>
                                <mjx-munder>
                                    <mjx-row>
                                        <mjx-base>
                                            <mjx-mo class="mjx-lop">
                                                <mjx-c class="mjx-c2211 TEX-S2"></mjx-c>
                                            </mjx-mo>
                                        </mjx-base>
                                    </mjx-row>
                                    <mjx-row>
                                        <mjx-under style="padding-top: 0.167em; padding-left: 0.086em;">
                                            <mjx-texatom size="s" texclass="ORD">
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                                </mjx-mi>
                                                <mjx-mo class="mjx-n">
                                                    <mjx-c class="mjx-c3D"></mjx-c>
                                                </mjx-mo>
                                                <mjx-mn class="mjx-n">
                                                    <mjx-c class="mjx-c31"></mjx-c>
                                                </mjx-mn>
                                            </mjx-texatom>
                                        </mjx-under>
                                    </mjx-row>
                                </mjx-munder>
                            </mjx-box>
                        </mjx-munderover>
                        <mjx-msubsup space="2">
                            <mjx-mi class="mjx-i">
                                <mjx-c class="mjx-c1D44E TEX-I"></mjx-c>
                            </mjx-mi>
                            <mjx-script style="vertical-align: -0.258em; margin-left: 0px;">
                                <mjx-mn class="mjx-n" size="s">
                                    <mjx-c class="mjx-c32"></mjx-c>
                                </mjx-mn>
                                <mjx-spacer style="margin-top: 0.18em;"></mjx-spacer>
                                <mjx-mi class="mjx-i" size="s">
                                    <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                </mjx-mi>
                            </mjx-script>
                        </mjx-msubsup>
                    </mjx-mrow>
                    <mjx-mo class="mjx-s4">
                        <mjx-c class="mjx-c29 TEX-S4"></mjx-c>
                    </mjx-mo>
                </mjx-mrow>
                <mjx-mrow space="2">
                    <mjx-mo class="mjx-s4">
                        <mjx-c class="mjx-c28 TEX-S4"></mjx-c>
                    </mjx-mo>
                    <mjx-mrow>
                        <mjx-munderover>
                            <mjx-over style="padding-bottom: 0.192em; padding-left: 0.51em;">
                                <mjx-mi class="mjx-i" size="s">
                                    <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                                </mjx-mi>
                            </mjx-over>
                            <mjx-box>
                                <mjx-munder>
                                    <mjx-row>
                                        <mjx-base>
                                            <mjx-mo class="mjx-lop">
                                                <mjx-c class="mjx-c2211 TEX-S2"></mjx-c>
                                            </mjx-mo>
                                        </mjx-base>
                                    </mjx-row>
                                    <mjx-row>
                                        <mjx-under style="padding-top: 0.167em; padding-left: 0.086em;">
                                            <mjx-texatom size="s" texclass="ORD">
                                                <mjx-mi class="mjx-i">
                                                    <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                                </mjx-mi>
                                                <mjx-mo class="mjx-n">
                                                    <mjx-c class="mjx-c3D"></mjx-c>
                                                </mjx-mo>
                                                <mjx-mn class="mjx-n">
                                                    <mjx-c class="mjx-c31"></mjx-c>
                                                </mjx-mn>
                                            </mjx-texatom>
                                        </mjx-under>
                                    </mjx-row>
                                </mjx-munder>
                            </mjx-box>
                        </mjx-munderover>
                        <mjx-msubsup space="2">
                            <mjx-mi class="mjx-i">
                                <mjx-c class="mjx-c1D44F TEX-I"></mjx-c>
                            </mjx-mi>
                            <mjx-script style="vertical-align: -0.258em; margin-left: 0px;">
                                <mjx-mn class="mjx-n" size="s">
                                    <mjx-c class="mjx-c32"></mjx-c>
                                </mjx-mn>
                                <mjx-spacer style="margin-top: 0.18em;"></mjx-spacer>
                                <mjx-mi class="mjx-i" size="s">
                                    <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                </mjx-mi>
                            </mjx-script>
                        </mjx-msubsup>
                    </mjx-mrow>
                    <mjx-mo class="mjx-s4">
                        <mjx-c class="mjx-c29 TEX-S4"></mjx-c>
                    </mjx-mo>
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            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <msup>
                    <mrow>
                        <mo>
                            (
                        </mo>
                        <mrow>
                            <munderover>
                                <mo>
                                    ∑
                                </mo>
                                <mrow data-mjx-texclass="ORD">
                                    <mi>
                                        k
                                    </mi>
                                    <mo>
                                        =
                                    </mo>
                                    <mn>
                                        1
                                    </mn>
                                </mrow>
                                <mi>
                                    n
                                </mi>
                            </munderover>
                            <msub>
                                <mi>
                                    a
                                </mi>
                                <mi>
                                    k
                                </mi>
                            </msub>
                            <msub>
                                <mi>
                                    b
                                </mi>
                                <mi>
                                    k
                                </mi>
                            </msub>
                        </mrow>
                        <mo>
                            )
                        </mo>
                    </mrow>
                    <mrow data-mjx-texclass="ORD">
                        <mspace width="negativethinmathspace"></mspace>
                        <mspace width="negativethinmathspace"></mspace>
                        <mn>
                            2
                        </mn>
                    </mrow>
                </msup>
                <mo>
                    ≤
                </mo>
                <mrow>
                    <mo>
                        (
                    </mo>
                    <mrow>
                        <munderover>
                            <mo>
                                ∑
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mi>
                                    k
                                </mi>
                                <mo>
                                    =
                                </mo>
                                <mn>
                                    1
                                </mn>
                            </mrow>
                            <mi>
                                n
                            </mi>
                        </munderover>
                        <msubsup>
                            <mi>
                                a
                            </mi>
                            <mi>
                                k
                            </mi>
                            <mn>
                                2
                            </mn>
                        </msubsup>
                    </mrow>
                    <mo>
                        )
                    </mo>
                </mrow>
                <mrow>
                    <mo>
                        (
                    </mo>
                    <mrow>
                        <munderover>
                            <mo>
                                ∑
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mi>
                                    k
                                </mi>
                                <mo>
                                    =
                                </mo>
                                <mn>
                                    1
                                </mn>
                            </mrow>
                            <mi>
                                n
                            </mi>
                        </munderover>
                        <msubsup>
                            <mi>
                                b
                            </mi>
                            <mi>
                                k
                            </mi>
                            <mn>
                                2
                            </mn>
                        </msubsup>
                    </mrow>
                    <mo>
                        )
                    </mo>
                </mrow></math>
            </mjx-assistive-mml>
        </mjx-container>
        <h2>
            A Cross Product Formula
        </h2>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" display="true" tabindex="0" ctxtmenu_counter="5" style="font-size: 101.6%; position: relative;">
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                        <mjx-table>
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                                        <mjx-tstrut></mjx-tstrut>
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                                    <mjx-mtd style="padding-left: 0.5em; padding-bottom: 0.2em;">
                                        <mjx-texatom texclass="ORD">
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                                                <mjx-c class="mjx-c1D424 TEX-B"></mjx-c>
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                                        <mjx-tstrut></mjx-tstrut>
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                                </mjx-mtr>
                                <mjx-mtr>
                                    <mjx-mtd style="padding-right: 0.5em; padding-top: 0.2em; padding-bottom: 0.2em;">
                                        <mjx-mfrac>
                                            <mjx-frac>
                                                <mjx-num>
                                                    <mjx-nstrut></mjx-nstrut>
                                                    <mjx-mrow size="s">
                                                        <mjx-mi class="mjx-n">
                                                            <mjx-c class="mjx-c2202"></mjx-c>
                                                        </mjx-mi>
                                                        <mjx-mi class="mjx-i">
                                                            <mjx-c class="mjx-c1D44B TEX-I"></mjx-c>
                                                        </mjx-mi>
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                                                </mjx-num>
                                                <mjx-dbox>
                                                    <mjx-dtable>
                                                        <mjx-line></mjx-line>
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                                                                <mjx-dstrut></mjx-dstrut>
                                                                <mjx-mrow size="s">
                                                                    <mjx-mi class="mjx-n">
                                                                        <mjx-c class="mjx-c2202"></mjx-c>
                                                                    </mjx-mi>
                                                                    <mjx-mi class="mjx-i">
                                                                        <mjx-c class="mjx-c1D462 TEX-I"></mjx-c>
                                                                    </mjx-mi>
                                                                </mjx-mrow>
                                                            </mjx-den>
                                                        </mjx-row>
                                                    </mjx-dtable>
                                                </mjx-dbox>
                                            </mjx-frac>
                                        </mjx-mfrac>
                                        <mjx-tstrut></mjx-tstrut>
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                                    <mjx-mtd style="padding: 0.2em 0.5em;">
                                        <mjx-mfrac>
                                            <mjx-frac>
                                                <mjx-num>
                                                    <mjx-nstrut></mjx-nstrut>
                                                    <mjx-mrow size="s">
                                                        <mjx-mi class="mjx-n">
                                                            <mjx-c class="mjx-c2202"></mjx-c>
                                                        </mjx-mi>
                                                        <mjx-mi class="mjx-i">
                                                            <mjx-c class="mjx-c1D44C TEX-I"></mjx-c>
                                                        </mjx-mi>
                                                    </mjx-mrow>
                                                </mjx-num>
                                                <mjx-dbox>
                                                    <mjx-dtable>
                                                        <mjx-line></mjx-line>
                                                        <mjx-row>
                                                            <mjx-den>
                                                                <mjx-dstrut></mjx-dstrut>
                                                                <mjx-mrow size="s">
                                                                    <mjx-mi class="mjx-n">
                                                                        <mjx-c class="mjx-c2202"></mjx-c>
                                                                    </mjx-mi>
                                                                    <mjx-mi class="mjx-i">
                                                                        <mjx-c class="mjx-c1D462 TEX-I"></mjx-c>
                                                                    </mjx-mi>
                                                                </mjx-mrow>
                                                            </mjx-den>
                                                        </mjx-row>
                                                    </mjx-dtable>
                                                </mjx-dbox>
                                            </mjx-frac>
                                        </mjx-mfrac>
                                        <mjx-tstrut></mjx-tstrut>
                                    </mjx-mtd>
                                    <mjx-mtd style="padding-left: 0.5em; padding-top: 0.2em; padding-bottom: 0.2em;">
                                        <mjx-mn class="mjx-n">
                                            <mjx-c class="mjx-c30"></mjx-c>
                                        </mjx-mn>
                                        <mjx-tstrut></mjx-tstrut>
                                    </mjx-mtd>
                                </mjx-mtr>
                                <mjx-mtr>
                                    <mjx-mtd style="padding-right: 0.5em; padding-top: 0.2em;">
                                        <mjx-mfrac>
                                            <mjx-frac>
                                                <mjx-num>
                                                    <mjx-nstrut></mjx-nstrut>
                                                    <mjx-mrow size="s">
                                                        <mjx-mi class="mjx-n">
                                                            <mjx-c class="mjx-c2202"></mjx-c>
                                                        </mjx-mi>
                                                        <mjx-mi class="mjx-i">
                                                            <mjx-c class="mjx-c1D44B TEX-I"></mjx-c>
                                                        </mjx-mi>
                                                    </mjx-mrow>
                                                </mjx-num>
                                                <mjx-dbox>
                                                    <mjx-dtable>
                                                        <mjx-line></mjx-line>
                                                        <mjx-row>
                                                            <mjx-den>
                                                                <mjx-dstrut></mjx-dstrut>
                                                                <mjx-mrow size="s">
                                                                    <mjx-mi class="mjx-n">
                                                                        <mjx-c class="mjx-c2202"></mjx-c>
                                                                    </mjx-mi>
                                                                    <mjx-mi class="mjx-i">
                                                                        <mjx-c class="mjx-c1D463 TEX-I"></mjx-c>
                                                                    </mjx-mi>
                                                                </mjx-mrow>
                                                            </mjx-den>
                                                        </mjx-row>
                                                    </mjx-dtable>
                                                </mjx-dbox>
                                            </mjx-frac>
                                        </mjx-mfrac>
                                        <mjx-tstrut></mjx-tstrut>
                                    </mjx-mtd>
                                    <mjx-mtd style="padding-left: 0.5em; padding-right: 0.5em; padding-top: 0.2em;">
                                        <mjx-mfrac>
                                            <mjx-frac>
                                                <mjx-num>
                                                    <mjx-nstrut></mjx-nstrut>
                                                    <mjx-mrow size="s">
                                                        <mjx-mi class="mjx-n">
                                                            <mjx-c class="mjx-c2202"></mjx-c>
                                                        </mjx-mi>
                                                        <mjx-mi class="mjx-i">
                                                            <mjx-c class="mjx-c1D44C TEX-I"></mjx-c>
                                                        </mjx-mi>
                                                    </mjx-mrow>
                                                </mjx-num>
                                                <mjx-dbox>
                                                    <mjx-dtable>
                                                        <mjx-line></mjx-line>
                                                        <mjx-row>
                                                            <mjx-den>
                                                                <mjx-dstrut></mjx-dstrut>
                                                                <mjx-mrow size="s">
                                                                    <mjx-mi class="mjx-n">
                                                                        <mjx-c class="mjx-c2202"></mjx-c>
                                                                    </mjx-mi>
                                                                    <mjx-mi class="mjx-i">
                                                                        <mjx-c class="mjx-c1D463 TEX-I"></mjx-c>
                                                                    </mjx-mi>
                                                                </mjx-mrow>
                                                            </mjx-den>
                                                        </mjx-row>
                                                    </mjx-dtable>
                                                </mjx-dbox>
                                            </mjx-frac>
                                        </mjx-mfrac>
                                        <mjx-tstrut></mjx-tstrut>
                                    </mjx-mtd>
                                    <mjx-mtd style="padding-left: 0.5em; padding-top: 0.2em;">
                                        <mjx-mn class="mjx-n">
                                            <mjx-c class="mjx-c30"></mjx-c>
                                        </mjx-mn>
                                        <mjx-tstrut></mjx-tstrut>
                                    </mjx-mtd>
                                </mjx-mtr>
                            </mjx-itable>
                        </mjx-table>
                    </mjx-mtable>
                    <mjx-mo class="mjx-n">
                        <mjx-stretchy-v class="mjx-c7C" style="height: 4.321em; vertical-align: -1.911em;">
                            <mjx-ext>
                                <mjx-c></mjx-c>
                            </mjx-ext>
                            <mjx-mark></mjx-mark>
                        </mjx-stretchy-v>
                    </mjx-mo>
                </mjx-mrow>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <msub>
                    <mrow data-mjx-texclass="ORD">
                        <mi mathvariant="bold">
                            V
                        </mi>
                    </mrow>
                    <mn>
                        1
                    </mn>
                </msub>
                <mo>
                    ×
                </mo>
                <msub>
                    <mrow data-mjx-texclass="ORD">
                        <mi mathvariant="bold">
                            V
                        </mi>
                    </mrow>
                    <mn>
                        2
                    </mn>
                </msub>
                <mo>
                    =
                </mo>
                <mrow>
                    <mo>
                        |
                    </mo>
                    <mtable rowspacing="4pt" columnspacing="1em">
                        <mtr>
                            <mtd>
                                <mrow data-mjx-texclass="ORD">
                                    <mi mathvariant="bold">
                                        i
                                    </mi>
                                </mrow>
                            </mtd>
                            <mtd>
                                <mrow data-mjx-texclass="ORD">
                                    <mi mathvariant="bold">
                                        j
                                    </mi>
                                </mrow>
                            </mtd>
                            <mtd>
                                <mrow data-mjx-texclass="ORD">
                                    <mi mathvariant="bold">
                                        k
                                    </mi>
                                </mrow>
                            </mtd>
                        </mtr>
                        <mtr>
                            <mtd>
                                <mfrac>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            X
                                        </mi>
                                    </mrow>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            u
                                        </mi>
                                    </mrow>
                                </mfrac>
                            </mtd>
                            <mtd>
                                <mfrac>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            Y
                                        </mi>
                                    </mrow>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            u
                                        </mi>
                                    </mrow>
                                </mfrac>
                            </mtd>
                            <mtd>
                                <mn>
                                    0
                                </mn>
                            </mtd>
                        </mtr>
                        <mtr>
                            <mtd>
                                <mfrac>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            X
                                        </mi>
                                    </mrow>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            v
                                        </mi>
                                    </mrow>
                                </mfrac>
                            </mtd>
                            <mtd>
                                <mfrac>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            Y
                                        </mi>
                                    </mrow>
                                    <mrow>
                                        <mi mathvariant="normal">
                                            ∂
                                        </mi>
                                        <mi>
                                            v
                                        </mi>
                                    </mrow>
                                </mfrac>
                            </mtd>
                            <mtd>
                                <mn>
                                    0
                                </mn>
                            </mtd>
                        </mtr>
                    </mtable>
                    <mo>
                        |
                    </mo>
                </mrow></math>
            </mjx-assistive-mml>
        </mjx-container>
        <h2>
            The probability of getting
        </h2>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="6" style="font-size: 101.5%; position: relative;">
            <mjx-math class="MJX-TEX" aria-hidden="true">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                </mjx-mi>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="inline">
                <math xmlns="http://www.w3.org/1998/Math/MathML">
                <mi>
                    k
                </mi></math>
            </mjx-assistive-mml>
        </mjx-container>heads when flipping
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="7" style="font-size: 101.5%; position: relative;">
            <mjx-math class="MJX-TEX" aria-hidden="true">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                </mjx-mi>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="inline">
                <math xmlns="http://www.w3.org/1998/Math/MathML">
                <mi>
                    n
                </mi></math>
            </mjx-assistive-mml>
        </mjx-container>coins is:
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" display="true" tabindex="0" ctxtmenu_counter="8" style="font-size: 101.6%; position: relative;">
            <mjx-math display="true" class="MJX-TEX" aria-hidden="true" style="margin-left: 0px; margin-right: 0px;">
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D443 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n">
                    <mjx-c class="mjx-c28"></mjx-c>
                </mjx-mo>
                <mjx-mi class="mjx-i">
                    <mjx-c class="mjx-c1D438 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-mo class="mjx-n">
                    <mjx-c class="mjx-c29"></mjx-c>
                </mjx-mo>
                <mjx-mo class="mjx-n" space="4">
                    <mjx-c class="mjx-c3D"></mjx-c>
                </mjx-mo>
                <mjx-texatom space="4" texclass="ORD">
                    <mjx-mrow>
                        <mjx-texatom texclass="OPEN">
                            <mjx-mo class="mjx-s3">
                                <mjx-c class="mjx-c28 TEX-S3"></mjx-c>
                            </mjx-mo>
                        </mjx-texatom>
                        <mjx-mfrac>
                            <mjx-frac type="d" atop="true" style="vertical-align: -0.686em;">
                                <mjx-num style="padding-bottom: 0.657em;">
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                                    </mjx-mi>
                                </mjx-num>
                                <mjx-den>
                                    <mjx-mi class="mjx-i">
                                        <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                                    </mjx-mi>
                                </mjx-den>
                            </mjx-frac>
                        </mjx-mfrac>
                        <mjx-texatom texclass="CLOSE">
                            <mjx-mo class="mjx-s3">
                                <mjx-c class="mjx-c29 TEX-S3"></mjx-c>
                            </mjx-mo>
                        </mjx-texatom>
                    </mjx-mrow>
                </mjx-texatom>
                <mjx-msup>
                    <mjx-mi class="mjx-i">
                        <mjx-c class="mjx-c1D45D TEX-I"></mjx-c>
                    </mjx-mi>
                    <mjx-script style="vertical-align: 0.413em;">
                        <mjx-mi class="mjx-i" size="s">
                            <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                        </mjx-mi>
                    </mjx-script>
                </mjx-msup>
                <mjx-mo class="mjx-n">
                    <mjx-c class="mjx-c28"></mjx-c>
                </mjx-mo>
                <mjx-mn class="mjx-n">
                    <mjx-c class="mjx-c31"></mjx-c>
                </mjx-mn>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c2212"></mjx-c>
                </mjx-mo>
                <mjx-mi class="mjx-i" space="3">
                    <mjx-c class="mjx-c1D45D TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-msup>
                    <mjx-mo class="mjx-n">
                        <mjx-c class="mjx-c29"></mjx-c>
                    </mjx-mo>
                    <mjx-script style="vertical-align: 0.413em;">
                        <mjx-texatom size="s" texclass="ORD">
                            <mjx-mi class="mjx-i">
                                <mjx-c class="mjx-c1D45B TEX-I"></mjx-c>
                            </mjx-mi>
                            <mjx-mo class="mjx-n">
                                <mjx-c class="mjx-c2212"></mjx-c>
                            </mjx-mo>
                            <mjx-mi class="mjx-i">
                                <mjx-c class="mjx-c1D458 TEX-I"></mjx-c>
                            </mjx-mi>
                        </mjx-texatom>
                    </mjx-script>
                </mjx-msup>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <mi>
                    P
                </mi>
                <mo stretchy="false">
                    (
                </mo>
                <mi>
                    E
                </mi>
                <mo stretchy="false">
                    )
                </mo>
                <mo>
                    =
                </mo>
                <mrow data-mjx-texclass="ORD">
                    <mrow>
                        <mrow data-mjx-texclass="OPEN">
                            <mo maxsize="2.047em" minsize="2.047em">
                                (
                            </mo>
                        </mrow>
                        <mfrac linethickness="0">
                            <mi>
                                n
                            </mi>
                            <mi>
                                k
                            </mi>
                        </mfrac>
                        <mrow data-mjx-texclass="CLOSE">
                            <mo maxsize="2.047em" minsize="2.047em">
                                )
                            </mo>
                        </mrow>
                    </mrow>
                </mrow>
                <msup>
                    <mi>
                        p
                    </mi>
                    <mi>
                        k
                    </mi>
                </msup>
                <mo stretchy="false">
                    (
                </mo>
                <mn>
                    1
                </mn>
                <mo>
                    −
                </mo>
                <mi>
                    p
                </mi>
                <msup>
                    <mo stretchy="false">
                        )
                    </mo>
                    <mrow data-mjx-texclass="ORD">
                        <mi>
                            n
                        </mi>
                        <mo>
                            −
                        </mo>
                        <mi>
                            k
                        </mi>
                    </mrow>
                </msup></math>
            </mjx-assistive-mml>
        </mjx-container>
        <h2>
            An Identity of Ramanujan
        </h2>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" display="true" tabindex="0" ctxtmenu_counter="9" style="font-size: 101.6%; position: relative;">
            <mjx-math display="true" class="MJX-TEX" aria-hidden="true" style="margin-left: 0px; margin-right: 0px;">
                <mjx-mfrac>
                    <mjx-frac type="d">
                        <mjx-num>
                            <mjx-nstrut type="d"></mjx-nstrut>
                            <mjx-mn class="mjx-n">
                                <mjx-c class="mjx-c31"></mjx-c>
                            </mjx-mn>
                        </mjx-num>
                        <mjx-dbox>
                            <mjx-dtable>
                                <mjx-line type="d"></mjx-line>
                                <mjx-row>
                                    <mjx-den>
                                        <mjx-dstrut type="d"></mjx-dstrut>
                                        <mjx-mrow>
                                            <mjx-mo class="mjx-n">
                                                <mjx-c class="mjx-c28"></mjx-c>
                                            </mjx-mo>
                                            <mjx-msqrt>
                                                <mjx-sqrt>
                                                    <mjx-surd>
                                                        <mjx-mo class="mjx-lop">
                                                            <mjx-c class="mjx-c221A TEX-S2"></mjx-c>
                                                        </mjx-mo>
                                                    </mjx-surd>
                                                    <mjx-box style="padding-top: 0.33em;">
                                                        <mjx-mi class="mjx-i">
                                                            <mjx-c class="mjx-c1D719 TEX-I"></mjx-c>
                                                        </mjx-mi>
                                                        <mjx-msqrt>
                                                            <mjx-sqrt>
                                                                <mjx-surd>
                                                                    <mjx-mo class="mjx-n">
                                                                        <mjx-c class="mjx-c221A"></mjx-c>
                                                                    </mjx-mo>
                                                                </mjx-surd>
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        <h2>
            A Rogers-Ramanujan Identity
        </h2>
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                                                            <mjx-c class="mjx-c2B"></mjx-c>
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                                                        <mjx-mn class="mjx-n">
                                                            <mjx-c class="mjx-c32"></mjx-c>
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                                            <mjx-mo class="mjx-n">
                                                <mjx-c class="mjx-c28"></mjx-c>
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                                            <mjx-mn class="mjx-n">
                                                <mjx-c class="mjx-c31"></mjx-c>
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                                                <mjx-c class="mjx-c2212"></mjx-c>
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                                                    <mjx-c class="mjx-c1D45E TEX-I"></mjx-c>
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                            (
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                        <mn>
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                        <mn>
                            6
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                            (
                        </mo>
                        <mn>
                            1
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                        <mi>
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                        </mi>
                        <mo stretchy="false">
                            )
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                        <mo stretchy="false">
                            (
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                        <mn>
                            1
                        </mn>
                        <mo>
                            −
                        </mo>
                        <msup>
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                            <mn>
                                2
                            </mn>
                        </msup>
                        <mo stretchy="false">
                            )
                        </mo>
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                    +
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                <mo>
                    ⋯
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                <mo>
                    =
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                        ∏
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                            =
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                        <mn>
                            0
                        </mn>
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                    <mrow data-mjx-texclass="ORD">
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                            ∞
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                        1
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                            (
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                            −
                        </mo>
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                                q
                            </mi>
                            <mrow data-mjx-texclass="ORD">
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                                    5
                                </mn>
                                <mi>
                                    j
                                </mi>
                                <mo>
                                    +
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                                <mn>
                                    2
                                </mn>
                            </mrow>
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                            )
                        </mo>
                        <mo stretchy="false">
                            (
                        </mo>
                        <mn>
                            1
                        </mn>
                        <mo>
                            −
                        </mo>
                        <msup>
                            <mi>
                                q
                            </mi>
                            <mrow data-mjx-texclass="ORD">
                                <mn>
                                    5
                                </mn>
                                <mi>
                                    j
                                </mi>
                                <mo>
                                    +
                                </mo>
                                <mn>
                                    3
                                </mn>
                            </mrow>
                        </msup>
                        <mo stretchy="false">
                            )
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                <mo>
                    ,
                </mo>
                <mspace width="1em"></mspace>
                <mspace width="1em"></mspace>
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                    <mtext>
                        for&nbsp;
                    </mtext>
                    <mrow data-mjx-texclass="ORD">
                        <mrow data-mjx-texclass="ORD">
                            <mo stretchy="false">
                                |
                            </mo>
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                            q
                        </mi>
                        <mrow data-mjx-texclass="ORD">
                            <mo stretchy="false">
                                |
                            </mo>
                        </mrow>
                        <mo>
                            &lt;
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                            1
                        </mn>
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                <mo>
                    .
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        </mjx-container>
        <h2>
            Maxwell's Equations
        </h2>
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                                            <mjx-over style="padding-bottom: 0.105em; padding-left: 0.287em; margin-bottom: -0.516em;">
                                                <mjx-mo class="mjx-n" style="width: 0px; margin-left: -0.25em;">
                                                    <mjx-c class="mjx-c20D7 TEX-V"></mjx-c>
                                                </mjx-mo>
                                            </mjx-over>
                                            <mjx-base>
                                                <mjx-texatom texclass="ORD">
                                                    <mjx-mn class="mjx-b">
                                                        <mjx-c class="mjx-c1D7CE TEX-B"></mjx-c>
                                                    </mjx-mn>
                                                </mjx-texatom>
                                            </mjx-base>
                                        </mjx-mover>
                                    </mjx-texatom>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                            </mjx-mtr>
                            <mjx-mtr>
                                <mjx-mtd style="text-align: right; padding-right: 0px; padding-top: 0.15em;">
                                    <mjx-mi class="mjx-n">
                                        <mjx-c class="mjx-c2207"></mjx-c>
                                    </mjx-mi>
                                    <mjx-mo class="mjx-n" space="3">
                                        <mjx-c class="mjx-c22C5"></mjx-c>
                                    </mjx-mo>
                                    <mjx-texatom space="3" texclass="ORD">
                                        <mjx-mover>
                                            <mjx-over style="padding-bottom: 0.105em; padding-left: 0.409em; margin-bottom: -0.516em;">
                                                <mjx-mo class="mjx-n" style="width: 0px; margin-left: -0.25em;">
                                                    <mjx-c class="mjx-c20D7 TEX-V"></mjx-c>
                                                </mjx-mo>
                                            </mjx-over>
                                            <mjx-base>
                                                <mjx-texatom texclass="ORD">
                                                    <mjx-mi class="mjx-b">
                                                        <mjx-c class="mjx-c1D401 TEX-B"></mjx-c>
                                                    </mjx-mi>
                                                </mjx-texatom>
                                            </mjx-base>
                                        </mjx-mover>
                                    </mjx-texatom>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                                <mjx-mtd style="text-align: left; padding-left: 0px; padding-top: 0.15em;">
                                    <mjx-mi class="mjx-n"></mjx-mi>
                                    <mjx-mo class="mjx-n" space="4">
                                        <mjx-c class="mjx-c3D"></mjx-c>
                                    </mjx-mo>
                                    <mjx-mn class="mjx-n" space="4">
                                        <mjx-c class="mjx-c30"></mjx-c>
                                    </mjx-mn>
                                    <mjx-tstrut></mjx-tstrut>
                                </mjx-mtd>
                            </mjx-mtr>
                        </mjx-itable>
                    </mjx-table>
                </mjx-mtable>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="block">
                <math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
                <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
                    <mtr>
                        <mtd>
                            <mi mathvariant="normal">
                                ∇
                            </mi>
                            <mo>
                                ×
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mi mathvariant="bold">
                                            B
                                        </mi>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                            <mo>
                                −
                            </mo>
                            <mspace width="thinmathspace"></mspace>
                            <mfrac>
                                <mn>
                                    1
                                </mn>
                                <mi>
                                    c
                                </mi>
                            </mfrac>
                            <mspace width="thinmathspace"></mspace>
                            <mfrac>
                                <mrow>
                                    <mi mathvariant="normal">
                                        ∂
                                    </mi>
                                    <mrow data-mjx-texclass="ORD">
                                        <mover>
                                            <mrow data-mjx-texclass="ORD">
                                                <mi mathvariant="bold">
                                                    E
                                                </mi>
                                            </mrow>
                                            <mo stretchy="false">
                                                →
                                            </mo>
                                        </mover>
                                    </mrow>
                                </mrow>
                                <mrow>
                                    <mi mathvariant="normal">
                                        ∂
                                    </mi>
                                    <mi>
                                        t
                                    </mi>
                                </mrow>
                            </mfrac>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mfrac>
                                <mrow>
                                    <mn>
                                        4
                                    </mn>
                                    <mi>
                                        π
                                    </mi>
                                </mrow>
                                <mi>
                                    c
                                </mi>
                            </mfrac>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mi mathvariant="bold">
                                            j
                                        </mi>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                    </mtr>
                    <mtr>
                        <mtd>
                            <mi mathvariant="normal">
                                ∇
                            </mi>
                            <mo>
                                ⋅
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mi mathvariant="bold">
                                            E
                                        </mi>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mn>
                                4
                            </mn>
                            <mi>
                                π
                            </mi>
                            <mi>
                                ρ
                            </mi>
                        </mtd>
                    </mtr>
                    <mtr>
                        <mtd>
                            <mi mathvariant="normal">
                                ∇
                            </mi>
                            <mo>
                                ×
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mi mathvariant="bold">
                                            E
                                        </mi>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                            <mspace width="thinmathspace"></mspace>
                            <mo>
                                +
                            </mo>
                            <mspace width="thinmathspace"></mspace>
                            <mfrac>
                                <mn>
                                    1
                                </mn>
                                <mi>
                                    c
                                </mi>
                            </mfrac>
                            <mspace width="thinmathspace"></mspace>
                            <mfrac>
                                <mrow>
                                    <mi mathvariant="normal">
                                        ∂
                                    </mi>
                                    <mrow data-mjx-texclass="ORD">
                                        <mover>
                                            <mrow data-mjx-texclass="ORD">
                                                <mi mathvariant="bold">
                                                    B
                                                </mi>
                                            </mrow>
                                            <mo stretchy="false">
                                                →
                                            </mo>
                                        </mover>
                                    </mrow>
                                </mrow>
                                <mrow>
                                    <mi mathvariant="normal">
                                        ∂
                                    </mi>
                                    <mi>
                                        t
                                    </mi>
                                </mrow>
                            </mfrac>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mn mathvariant="bold">
                                            0
                                        </mn>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                    </mtr>
                    <mtr>
                        <mtd>
                            <mi mathvariant="normal">
                                ∇
                            </mi>
                            <mo>
                                ⋅
                            </mo>
                            <mrow data-mjx-texclass="ORD">
                                <mover>
                                    <mrow data-mjx-texclass="ORD">
                                        <mi mathvariant="bold">
                                            B
                                        </mi>
                                    </mrow>
                                    <mo stretchy="false">
                                        →
                                    </mo>
                                </mover>
                            </mrow>
                        </mtd>
                        <mtd>
                            <mi></mi>
                            <mo>
                                =
                            </mo>
                            <mn>
                                0
                            </mn>
                        </mtd>
                    </mtr>
                </mtable></math>
            </mjx-assistive-mml>
        </mjx-container>
        <h2>
            In-line Mathematics
        </h2>
        <p>
            Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression
        </p>
        <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="12" style="font-size: 101.6%; position: relative;">
            <mjx-math class="MJX-TEX" aria-hidden="true">
                <mjx-msqrt>
                    <mjx-sqrt>
                        <mjx-surd>
                            <mjx-mo class="mjx-n">
                                <mjx-c class="mjx-c221A"></mjx-c>
                            </mjx-mo>
                        </mjx-surd>
                        <mjx-box style="padding-top: 0.134em;">
                            <mjx-mn class="mjx-n">
                                <mjx-c class="mjx-c33"></mjx-c>
                            </mjx-mn>
                            <mjx-mi class="mjx-i">
                                <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                            </mjx-mi>
                            <mjx-mo class="mjx-n" space="3">
                                <mjx-c class="mjx-c2212"></mjx-c>
                            </mjx-mo>
                            <mjx-mn class="mjx-n" space="3">
                                <mjx-c class="mjx-c31"></mjx-c>
                            </mjx-mn>
                        </mjx-box>
                    </mjx-sqrt>
                </mjx-msqrt>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c2B"></mjx-c>
                </mjx-mo>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c28"></mjx-c>
                </mjx-mo>
                <mjx-mn class="mjx-n">
                    <mjx-c class="mjx-c31"></mjx-c>
                </mjx-mn>
                <mjx-mo class="mjx-n" space="3">
                    <mjx-c class="mjx-c2B"></mjx-c>
                </mjx-mo>
                <mjx-mi class="mjx-i" space="3">
                    <mjx-c class="mjx-c1D465 TEX-I"></mjx-c>
                </mjx-mi>
                <mjx-msup>
                    <mjx-mo class="mjx-n">
                        <mjx-c class="mjx-c29"></mjx-c>
                    </mjx-mo>
                    <mjx-script style="vertical-align: 0.363em;">
                        <mjx-mn class="mjx-n" size="s">
                            <mjx-c class="mjx-c32"></mjx-c>
                        </mjx-mn>
                    </mjx-script>
                </mjx-msup>
            </mjx-math>
            <mjx-assistive-mml unselectable="on" display="inline">
                <math xmlns="http://www.w3.org/1998/Math/MathML">
                <msqrt>
                    <mn>
                        3
                    </mn>
                    <mi>
                        x
                    </mi>
                    <mo>
                        −
                    </mo>
                    <mn>
                        1
                    </mn>
                </msqrt>
                <mo>
                    +
                </mo>
                <mo stretchy="false">
                    (
                </mo>
                <mn>
                    1
                </mn>
                <mo>
                    +
                </mo>
                <mi>
                    x
                </mi>
                <msup>
                    <mo stretchy="false">
                        )
                    </mo>
                    <mn>
                        2
                    </mn>
                </msup></math>
            </mjx-assistive-mml>
        </mjx-container>is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.
    </body>
</html>
